Lie algebra automorphism

Inner Lie algebra automorphism

An inner automorphism of a Lie algebra is given by , where is the adjoint representation for some . lie As the Exponential of a derivation on a Lie algebra it is an automorphism.¹ The set of all inner automorphisms forms a normal subgroup of .

Proof of normal subgroup

proof

---

develop | en | sembr

Footnotes

1. 1972. Introduction to Lie Algebras and Representation Theory, §2.3, pp. 8–9 ↩